{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.fftpack import fft\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fourier_transform(actions, T=0.002):\n",
    "    N = len(actions)\n",
    "    # print(N)\n",
    "    x = np.linspace(0.0, N*T, N)\n",
    "    y = actions\n",
    "    yf = fft(y)\n",
    "    freq = np.linspace(0.0, 1.0/(2.0*T), N//2)\n",
    "    amplitudes = 2.0/N * np.abs(yf[0:N//2])\n",
    "    # plt.plot(freq, amplitudes)\n",
    "    return freq, amplitudes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Fs = 1e4      # 采样频率\n",
    "f1 = 390       # 信号频率1\n",
    "f2 = 2e3      # 信号频率2\n",
    "t=np.linspace(0., 1., int(Fs))   # 生成 1s 的实践序列   \n",
    "noise1 = np.random.random(int(1e4))      # 0-1 之间的随机噪声\n",
    "noise2 = np.random.normal(1.,10.,int(1e4))\n",
    "#产生的是一个10e3的高斯噪声点数组集合（均值为：1，标准差：10）\n",
    "y=2*np.sin(2*np.pi*f1*t)+5*np.sin(2*np.pi*f2*t)+noise2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "4982.996599319864 0.03177475745430353\n",
      "4983.996799359872 0.18192497222375464\n",
      "4984.996999399879 0.10415307560983797\n",
      "4985.9971994398875 0.1154601213578167\n",
      "4986.997399479896 0.26741716345092137\n",
      "4987.997599519904 0.17421115005853557\n",
      "4988.997799559912 0.22782712151312545\n",
      "4989.99799959992 0.1751747793679348\n",
      "4990.998199639927 0.08002344323239478\n",
      "4991.998399679936 0.08519671519416407\n",
      "4992.998599719944 0.2557216825452869\n",
      "4993.998799759952 0.32704080624142656\n",
      "4994.99899979996 0.33843876695884423\n",
      "4995.999199839967 0.2347915880404242\n",
      "4996.9993998799755 0.11736121550054297\n",
      "4997.999599919984 0.12769553947623205\n",
      "4998.999799959992 0.14885742900877383\n",
      "5000.0 0.2446450382153081\n"
     ]
    }
   ],
   "source": [
    "freqs, amps = fourier_transform(y, T=1/Fs)\n",
    "for a, b in zip(freqs, amps):\n",
    "    print(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7efdd894fca0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(freqs, amps)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "dcs_py38",
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